THERMODYNAMICS OF ATMOSPHERE VON BEZOLD 259 



Consequently 



80 y, = (1000 - y t ) c v t + 0.51 y x t 



since 0.51 is the specific heat of ice, 



Since c v lies between the limits 0.1693 an d 0.1701 under the condi- 

 tions here considered we can substitute 0.17 for this value and 

 obtain 



or 



whence 



80 y x = (1000 - y x ) X 0.17 * + 0.51 y x t 

 80 y x --= (170 + 0.34 y x ) t 



80 8 1 



1 = 170 + 0.34 yj l == 17 1 + 0.002 yj v 



By developing into a series the fraction containing y x in the 

 denominator and retaining only the first two terms we obtain 



t = 0.4706 y + 0.00094 y* 



Since 10 is a high value for y x that is not likely to be exceeded, 

 and since the second term attains only the value o.i°C. when y x = 10, 

 therefore we may ordinarily confine ourselves to the use of the first 

 term of this equation. 



The formula just given enables us to compute the temperature / 

 that prevails immediately after the sudden freezing occurs through- 

 out the whole of a subcooled mass, assuming that t 2 is below freezing, 

 that is to say, that /, < 0. 



If this assumption does not hold good, then the computed value 

 loses its significance and the value must be substituted for it, no 

 matter how large y x may be. 



In this case only a part y x * of the subcooled water can be frozen, 

 which part will evidently be given by the equation 



t x = 0.4706 y* 



where for simplicity we have omitted the second correction term. 

 We have now still to consider how to determine the final tem- 

 perature £ 3 as it must result when the air, which was no longer satu- 

 rated at the moment of freezing, becomes again saturated with 

 aqueous vapor. For although as above remarked, the final condi- 

 tion is not of importance with reference to the sudden rise in pressure 

 which is at present our first consideration, since the pressure must 



